Teamwork and Problem Solving: ActivitiesENGR 1181Class 2 – Part 2

Teamwork: ActivityThe Challenge: Using only four 4s, create mathematical expressions that create integers. Start with 0 and work your way up. (e.g., equations equal to 0,1,2,3,4,5…)

The Rules: You can use only four 4s, but you may use unlimited symbols or operators. Possible operators include: + - ! ^ ÷ × √ ( )

Four Fours: Examples0 = 4-4+4-4

1 = (4+4)/(4+4)

2 = …

3 = …

4 = …

Four Fours: Individual WorkWorking on your own, see how many equations you can come up with in three minutes. Calculators are permitted.

Time starts now!

How many equations did you successfully create?

What was the highest integer you were able to solve for?

Four Fours: Team WorkNow, see how many equations you can create when you work together with your teammates.

Time starts now!

How many equations did you successfully create?

Were you able to create more as a team?

Do you think that teamwork helped to solve this problem?

Problem Solving: ActivityLet’s work through a sample problem together.

Problem: Determine how much paint is needed to paint a room that is 16’x 20’ with a 10 foot ceiling.

Given Info: There are two windows and two doors, and the room needs two coats of paint.

1. Define Sample ProblemIdentify the Goal:

Determine the number of gallons of paint needed to paint the room.

Identify Constraints:

Two coats of paint

1. Define Sample Problem

Known:

Length: 16 ft

Width: 20 ft

Height: 10 ft

Two doors

Two windows

Unknown:

Are doors painted?

Are windows painted?

Use the same paint as wall?

Dimensions of doors?

Dimensions of windows?

Document known and unknown information:

1. Define Sample ProblemDocument assumptions, estimates, and research:

The ceiling of the room will also be painted

The same paint will be used for walls and ceiling

Doors are not painted

Windows are not painted

Size of doors and windows

Coverage of paint (thick/thin)

2. Represent Sample Problem

Note: Ceiling height is 10 ft.

3. Plan Sample ProblemIdentify the underlying principle(s):

Geometry Problem (area calculations)

Rate Problem (paint coverage)

Recognize similarities and differences of the problem:

Area calculations: find surface areaArea = length x width = Areawalls + Areaceiling - Areawindows- Areadoors

3. Plan Sample ProblemPaint Coverage: calculate needed gallons of paint

Gallons = # Coats x Area (ft2)

Coverage (ft2/gal)

3. Plan Sample ProblemIdentify tools to be used:

Calculator, spreadsheet, pencil, iPhone app, etc.

Make assumptions or estimates:

Area of door: 7 ft x 3 ft = 21 ft2 per door

Area of window: 3 ft x 5 ft = 15 ft2 per window

Paint Coverage: 320 ft2 per gallon

4. Implement Sample ProblemExecute the Plan!Painted Area = Areawalls + Areaceiling - Areawindows- Areadoors

Painted Area = 968 ft2

4. Implement Sample Problem

Execute the Plan! (continued)

Gallons of Paint = # Coats x Area

(ft2)

Coverage (ft2/gal)

Gallons of Paint = 6.1 Gallons

5. Evaluate Sample ProblemDoes 6.1 gallons of paint make sense?

Does it answer the original question?

Are the units appropriate?

Is 6.1 gallons an appropriate scale?

What about lost/wasted paint?

Is the paint coverage rate reasonable? What did this include? (i.e., type of surface)

5. Evaluate Sample ProblemTo verify our calculations, can we use other approaches involving the same variables?

Yes! One possible way is:

1. Calculate a total length for the walls and multiply by the height to find total area.

2. Calculate gallons of paint for each all walls and the ceiling.

3. Add up total paint needed.

5. Evaluate Sample Problem

• Now that we have an acceptable answer, we need to present it clearly in the appropriate format.

• Sometimes this includes a graph or chart

• With this example, we can simply state the answer in a complete, descriptive sentence:

“6.1 gallons of paint is required to paint the walls and ceiling of the room, given the assumptions above.”

Homework Assignment Let’s look at the assignment together.

What is the problem statement?

What is known information?

What is unknown?

How could we represent the problem?

Important Takeaways Teamwork makes problem solving easier,

but…it takes work to make a good team work well.

Preview of Next Class Ethics + Academic Integrity

What’s Next? Review today’s lecture.

Open the in-class activity from the EEIC website and we will go through it together.

Then, start working on homework.